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The diameters of two silver discs are in the ratio 2:3 . What Will be the ratio of their areas
Given:
The diameters of two silver discs are in the ratio 2:3.
To do:
We have to find the ratio of their areas.
Solution:
Let the radius of the two discs be $r_1$ and $r_2$.
We know that,
Area of a circle of radius $r=\pi r^2$
Therefore,
Ratio of the diameters $=2r_1:2r_2$
$\Rightarrow r_1:r_2=2:3$
Ratio of the areas of the circles $=\frac{22}{7} \times(r_1)^{2}:\frac{22}{7} \times(r_2)^{2}$
$=r_1^2:r_2^2$
$=(\frac{r_1}{r_2})^2$
$=(\frac{2}{3})^2$
$=\frac{4}{9}$
The ratio of the areas of the discs is $4:9$.
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